Final answer:
The depth of water in the rectangular container after being poured from the cylindrical container is 24 cm, none of the provided multiple choice options are correct.
Step-by-step explanation:
To solve this problem, we use the concept of conservation of volume. The amount of water in the cylindrical container will be the same when transferred to the rectangular container. Since the volume of a cylinder is given by V = πr²h and the volume of a rectangular prism is given by V = lwh, we can equate both volumes to find the unknown height of water in the rectangular container.
The volume of the cylindrical container can be calculated using the given height (28 cm) and diameter (18 cm). The diameter gives us the radius by taking half of it, which is 9 cm. Thus, we get the volume of the cylindrical container:
V_cylinder = π * (9 cm)² * 28 cm
Using π as 22/7, we calculate the volume:
V_cylinder = 22/7 * 81 cm² * 28 cm = 22 * 81 * 4 cm³ = 7128 cm³
Now, we pour the water into the rectangular container. The volume in this container will remain 7128 cm³, so we use the formula for the volume of a rectangular prism and solve for the height (h_rect):
V_rectangular_prism = l * w * h_rect = 27 cm * 11 cm * h_rect = 7128 cm³
Now solve for h_rect:
h_rect = 7128 cm³ / (27 cm * 11 cm) = 7128 cm³ / 297 cm² = 24 cm
We find that the depth of water in the rectangular container is 24 cm, which means none of the provided options a) 6 cm, b) 7 cm, c) 8 cm, d) 9 cm are correct. The correct depth is not listed among those options.